# An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Network Model and Assumptions

- The term sensor area, denoted as $\sum $, not only refers to the geographical area covered by the WSN but also to the set of nodes in this area. We denote an event region as $\mathsf{\omega}$, which is the sub-region of $\sum $ covered by an event and $\mathsf{\varpi}$ is the remaining region. Thus, $\sum =\mathsf{\omega}+\mathsf{\varpi}$. Hence, a sensor node ${S}_{i}\in \mathsf{\omega}$ means it is an affected node while ${S}_{i}\in \mathsf{\varpi}$ means it is a normal node.
- A sensor node ${S}_{i}$ with its location information, that is ${S}_{i}(xi,yi)$, is considered to be a boundary node when it is on the actual boundary. Let us consider a boundary width $R$ defined as the communication radius of the sensor ${S}_{i}$ according to [13]. Let $N({S}_{i})$ denote the disk centred at node ${S}_{i}$ with the radius $R$. Therefore ${S}_{i}$ is a boundary node if $\Vert {S}_{i},B\Vert $≤ r where $\Vert {S}_{i},B\Vert $ is the geographic distance between ${S}_{i}$ and B the actual boundary. Then the event boundary $B({S}_{i})$ is the collection of such boundary nodes.

## 4. Proposed Algorithm

#### 4.1. The Statistical Boundary Detection Model

- H = 0 if and only if all the ${p}_{i}$ but one are null. This means that all the neighbours of ${S}_{i}$ are entirely affected or absolutely normal. Otherwise, if H is positive, that is, node ${S}_{i}$ has the probability to be a boundary node. The higher the value of H is, the closer the node is to the actual boundary.
- When all the ${p}_{i}$ are equal (i.e., p = q), the value of H is the largest and is log 2. This is also intuitively the higher probability a node to be a boundary node.
- Any change towards equalization of the probabilities p, q increases H.

#### 4.2. Determining Rules

Algorithm 1: Entropy based Event Boundary Detection (EEBD) Algorithm |

Input$:\text{}\mathrm{Node}\text{}{S}_{i}$$,\text{}\mathrm{boundary}\text{}\mathrm{width}\text{}r$, node density ρ$,\text{}\mathrm{communication}\text{}\mathrm{radius}\text{}\mathrm{R}\text{}\mathrm{and}\text{}{M}_{{S}_{i}}=\left\{\right\}$ |

Output: broadcast the ID if it is the real event boundary senor node |

For each sensor node |

$\mathrm{Initialize}:\text{}\mathrm{compute}\text{}{H}_{th}$$\text{}\mathrm{according}\text{}\mathrm{to}\text{}\left(8\right),\text{}{H}_{i}=0$; |

step 1; |

Discover the affected sensor nodes |

if$\text{}\mathrm{sensing}\text{}\mathrm{data}\text{}\text{}{\mu}_{th}$ |

flag(i) ← 1 |

else |

flag(i) ← 0 |

end |

$\mathrm{Broadcast}\text{}{M}_{{S}_{i}}:=\left\{{S}_{i},{H}_{i},flag(i)\right\}$ to its neighbour nodes |

ifflag(i) == 1 |

${H}_{i}\leftarrow -(p\mathrm{log}p+q\mathrm{log}q)$ |

$\mathrm{Update}\text{}{M}_{{S}_{i}}$ $\mathrm{with}\text{}\mathrm{new}\text{}{H}_{i}$ |

end |

step 2; |

$\mathrm{Broadcast}\text{}\mathrm{message}{M}_{{S}_{i}}:=\left\{{S}_{i},{H}_{i},flag(i)\right\}$ |

Listen to its neighbour nodes |

step 3 |

if${H}_{i}\ge {H}_{th}$ |

$\text{}\mathrm{broadcast}\text{}{S}_{i}$ $\text{}\mathrm{as}\text{}\mathrm{the}\text{}\mathrm{final}\text{}\mathrm{boundary}\text{}\mathrm{node}\text{}\mathrm{to}\text{}\mathrm{the}\text{}\mathrm{sin}\mathrm{k},\text{}B({S}_{i},r)$ |

## 5. Simulation Results

#### 5.1. Simulation Initialization

#### 5.2. Simulation Results

#### 5.3. Efficiency Evaluation

## 6. Conclusions

- (1)
- To further decrease the sensor nodes’ energy consumption and extend network lifespan under the condition of ensuring the accuracy of event boundary detection, the energy consumption model and the event reporting routing protocol need further research.
- (2)
- A complete event dataset is necessary before the boundary detection algorithm is executed. Due to the adverse conditions of the sea, the collected marine big data always experience a serious data loss phenomenon in WSNs [22]. To further improve the accuracy of event boundary detection, the missing data recovery of WSNs is an important research topic.
- (3)
- Real marine event boundary detection experiments and event boundary dynamic tracking are also key research directions for the future.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 13.**The boundary detection rates of EEBD with different densities of marine mobile nodes. (

**a**) 50%. (

**b**) 60%. (

**c**) 70%. (

**d**) 80%.

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**MDPI and ACS Style**

Wu, H.; Meng, Q.; Xian, J.; Mei, X.; Claramunt, C.; Cao, J.
An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks. *Symmetry* **2019**, *11*, 537.
https://doi.org/10.3390/sym11040537

**AMA Style**

Wu H, Meng Q, Xian J, Mei X, Claramunt C, Cao J.
An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks. *Symmetry*. 2019; 11(4):537.
https://doi.org/10.3390/sym11040537

**Chicago/Turabian Style**

Wu, Huafeng, Qingshun Meng, Jiangfeng Xian, Xiaojun Mei, Christophe Claramunt, and Junkuo Cao.
2019. "An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks" *Symmetry* 11, no. 4: 537.
https://doi.org/10.3390/sym11040537